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A263103
Minimum possible number of cycles without repeated edges on a multigraph with 3 vertices and n edges (when each vertex pair must have at least one edge).
3
1, 3, 8, 28, 103, 415, 2176, 12888, 77787, 585411, 4616376, 37165472, 359048127, 3547499455, 35666828200, 418731250432, 4974631473123, 59967609426243, 827065614194184, 11481419054280168, 161364022042775615, 2553658998728779999
OFFSET
3,2
COMMENTS
Cycles have length at least 2, and may repeat vertices but not edges.
Cycles p,q are equivalent if the vertex-edge sequence of q can be made by rotating or reversing that of p. The multigraphs have no loops.
Edge arrangements which produce these numbers are given in A263104. Maximum possible number of cycles appears to be A263102(n-1), generated by edges arranged [1,1,n-2].
LINKS
Eric W. Weisstein, Multigraph
EXAMPLE
For n=6 there are three possible arrangements:
1,1,4: 40 cycles,
1,2,3: 28 cycles,
2,2,2: 33 cycles,
so a(6) = 28.
PROG
(Python) See links.
CROSSREFS
Sequence in context: A327015 A151431 A245892 * A093356 A224271 A135583
KEYWORD
nonn,walk,hard
AUTHOR
Simon R. Donnelly, Oct 09 2015
STATUS
approved